On the Hamiltonicity of triple systems with high minimum degree

TL;DR

This paper proves that 3-uniform hypergraphs with a high minimum degree threshold necessarily contain a tight Hamiltonian cycle, advancing understanding of Hamiltonicity conditions in hypergraphs.

Contribution

It establishes a new minimum degree condition (80%) that guarantees Hamiltonicity in 3-uniform hypergraphs, improving previous bounds.

Findings

Hypergraphs with minimum degree ≥ 0.8 * binom(n-1, 2) contain Hamiltonian cycles

Provides a new threshold for Hamiltonicity in 3-uniform hypergraphs

Enhances theoretical understanding of hypergraph Hamiltonian properties

Abstract

We show that every 3-uniform hypergraph with minimum vertex degree at least $0.8\binom{n-1}{2}$ contains a tight Hamiltonian cycle.